What is H0 what is H1

[pierrreg]

Hi

In this case:

'In order to test whether the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the sample value of the computed test statistic tn-1=34. If you choose a 5% significance level, what should you do?"

what is H0, what is Ha?

And in this case:

An analyst believes that the mean price of houses in the area is greater than 145000$. A random sample of 36 hours in hte area has a mean price of 149750. The population standar deviation is 24000$ and he wants to conduct a hypothesis test at a level of 1% of signifiance";

thank you

[tickersu]

@pierrreg

Hi

In this case:

'In order to test whether the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the sample value of the computed test statistic tn-1=34. If you choose a 5% significance level, what should you do?"

what is H0, what is Ha?

Ask yourself-- they are searching for evidence of something-- what is that “something”? In this case, they want to see if the mean IQ exceeds 100-- this is your alternative hypothesis, Ha. Since Ha: mu > 100, that means Ho: mu less than or equal to 100. How do we know this? First, Ho is assumed to be true until evidence suggests otherwise. Second, our tests will never lead us to “prove” Ho or say that Ho is true. How does this relate to our question? We want to see if there is evidence to suggest that mu exceeds 100, and since we know that we can find evidence in favor (or not in favor) of Ha, we should set Ha: mu > 100 (leaving the rest for Ho). In other words, we’re going to assume that the mean IQ score does not exceed 100 (Ho) until the data suggest that mu does exceed 100 (Ha).

@pierrreg

And in this case:

An analyst believes that the mean price of houses in the area is greater than 145000$. A random sample of 36 hours in hte area has a mean price of 149750. The population standar deviation is 24000$ and he wants to conduct a hypothesis test at a level of 1% of signifiance";

thank you

Lets try the same process as above. He wants to support his claim that mu > $145,000. Since we can (or cannot) find evidence to support of Ha, we should say that Ha: mu > $145000, which leaves Ho: mu less than or equal to $145000. Again, since you have this belief that mu exceeds 145000 (Ha), we should assume it doesn’t exceed 145000 (Ho) and look at the data to see if the data disagree with Ho in favor of Ha.

I hope this is helpful.

[pierrreg]

I think I got it. So in both case, H0 is the hypothèse we want to reject of disapprove. In the first case we want people of high IQ, so we want to disapprove the fact that they have small IQ;

In the second case, we the analyst want’s to have high house prices, so the hypothesis he want’s to reject is the fact that the average price is below 145000

So in the first cas: H0: mu<100: H1:mu>100

in the second case:

H0: mu<145000: H1:mu>145000

[tickersu]

@pierrreg

I think I got it. So in both case, H0 is the hypothèse we want to reject of disapprove.

You can think of it in this way, and it’ll probably get you the correct answer.

@pierrreg

In the first case we want people of high IQ, so we want to disapprove the fact that they have small IQ;

In the second case, we the analyst want’s to have high house prices, so the hypothesis he want’s to reject is the fact that the average price is below 145000

Just remember that you’ll always have an equals sign in Ho. This is where we assume our distribution is centered.

@pierrreg

So in the first cas: H0: _ mu < = 100 (practically, this is no different than mu= 100)_ : H1:mu>100

in the second case:

H0: mu < = 145000 (same as before, this is essentially mu = 145000) : H1:mu>145000

The key is that you remember the equals sign should be in Ho. You can remember this by thinking of a bell curve with the mean specified in Ho. We start by assuming the mean (center) of the distribution is 100, for example (like the first question). When we say Ho: mu = 100, we’re saying “let’s assume mu is 100 for our distribution. If the data are in strong disagreement with this, we will reject Ho because it appears that mu is different from 100 (Ha: mu not equal to 100).” This works for Ha of greater than or less than, too.

[pierrreg]

Than you for your answer.

I don’t know how skilled you are in math, but I would like to go further in the mathematics behind all those z-test and t-test.

Let’s take the example of the test ,

let’s denote alpha, the signficance level. let’s denote the statisical mean: mu: omega–>mu(omega) let’s denote x, the mean of the IQ

So we have: alpha=P(RejectH0|H0) (that is we reject H0 knowing H0 is true, it’s a conditional probability)

we can then rewrite this as: exists cv>100 such that: alpha=P({omega: mu(omega)>cv | x<=0})

then we can get read of the condition, make a variable change and we have: alpha=P({omega: (mu(omega)-x)/sigma>cv’})

Right?

[tickersu]

@pierrreg

Than you for your answer.

I don’t know how skilled you are in math, but I would like to go further in the mathematics behind all those z-test and t-test.

Let’s take the example of the test ,

let’s denote alpha, the signficance level. let’s denote the statisical mean: mu: omega–>mu(omega)

Is mu(omega) the assumed value for the null?

@pierrreg

let’s denote x, the mean of the IQ **

**Sample mean, correct?

@pierrreg

So we have: alpha=P(RejectH0|H0) (that is we reject H0 knowing H0 is true, it’s a conditional probability)

I’m familiar.

@pierrreg

we can then rewrite this as: exists cv >100 such that: alpha=P({omega: mu(omega)>cv | x<=0})

then we can get read of the condition, make a variable change and we have: alpha=P({omega: (mu(omega)-x)/sigma>cv’})

Right?

What are you defining “cv” as? If you make your notation a touch clearer, I might be able to directly answer your question. At a quick glance, though, it looks as though you’re trying to equate alpha and the p-value, which is not correct (p-value for a one-tailed (upper) test is P( Z >= z | Ho) where Z is some future test statistics and z is the current value) . If you answer some of my questions and help me with your notation, it would help me understand what you’re asking.